The millisecond time resolution of event-related potentials (ERPs) gives them a unique advantage in studying brain function, but ERP research is seriously limited by the lack of statistical methods to address the complexity and variability of ERP data. In this project, we will develop a new statistical approach to decomposition of ERP waveforms, analysis of the sources of variability, and estimation of the effects of experimental conditions and disease states. We will evaluate the new methods using simulated ERPs and many animal and human ERP data sets, including ERPs acquired from schizophrenic and stroke patients who also were studied using structural magnetic resonance imaging (MRI). The new statistical methods will combine time series modeling using the wavelet transform with nonlinear mixed effects models. Wavelet analysis decomposes ERPs by time and frequency. We have already validated our wavelet models in applications to simulated data, cat auditory evoked potentials, and human P300 potentials. Wavelet analysis separated superimposed components, yielding realistic condition effects and topographies, even in difficult cases in which principal components analysis failed. Our nonlinear mixed effects models will provide a parsimonious representation of the variability among individuals (human subjects or experimental animals) and single trials (responses to single stimulus presentations). They will yield valid significance tests and confidence intervals, extending familiar linear statistical procedures to complicated nonlinear time series. The specific aims of this project are to develop, evaluate, and apply the following statistical methods. 1. The Single Channel Wavelet Model will separate superimposed components in single channel average ERPs, and yield significance tests for condition effects on the amplitude and latency of each component. 2. The Topographic Wavelet Model will extend the single channel wavelet model to multichannel data, and provide estimated of the topography of each component. Regularization of the topography will allow analysis of ERPs from dense electrode arrays. 3. The Trial-Specific Wavelet Model will extend the single channel wavelet model to include both inter-individual and inter-trial variability, allowing estimation of the relationships among ERP components and between ERP components and trial-specific variables such as reaction time and subjective intensity.